Problem: Solve for $x$ and $y$ using elimination. ${x-4y = -18}$ ${-x+3y = 11}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x-4y = -18}\thinspace$ to find $x$ ${x - 4}{(7)}{= -18}$ $x-28 = -18$ $x-28{+28} = -18{+28}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {-x+3y = 11}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(7)}{= 11}$ ${x = 10}$